Related papers: Complete Graphs and Polyominoes
In this paper, we study the graph classification problem in vertex-labeled graphs. Our main goal is to classify the graphs comparing their higher-order structures thanks to heat diffusion on their simplices. We first represent…
A multiflow in a planar graph is uncrossed if its support paths do not cross. Recently such flows have played a role in approximation algorithms for maximum disjoint paths in "fully-planar" instances, where the combined supply-demand graph…
The burning and forcing processes are both instances of propagation processes on graphs that are commonly used to model real-world spreading phenomena. The contribution of this paper is two-fold. We first establish a connection between…
We study the spread of information on multi-type directed random graphs. In such graphs the vertices are partitioned into distinct types (communities) that have different transmission rates between themselves and with other types. We…
Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational…
We study the popular randomized rumour spreading protocol Push. Initially, a node in a graph possesses some information, which is then spread in a round based manner. In each round, each informed node chooses uniformly at random one of its…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
We show that two-dimensional fermions with dispersion $k^2$ or $k^4$ undergo a first-order Stoner transition to a fully spin-polarized state despite that the spin susceptibility diverges at the critical point. We extend our analysis to…
Diffusion probabilistic models (DPMs), widely recognized for their potential to generate high-quality samples, tend to go unnoticed in representation learning. While recent progress has highlighted their potential for capturing visual…
We consider (not necessarily proper) colorings of the vertices of a graph where every color is thoroughly distributed, that is, appears in every open neighborhood. Equivalently, every color is a total dominating set. We define $\td(G)$ as…
Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which…
The discrete Fourier transform and the FFT algorithm are extended from the circle to continuous graphs with equal edge lengths.
Diffusion probabilistic models excel at sampling new images from learned distributions. Originally motivated by drift-diffusion concepts from physics, they apply image perturbations such as noise and blur in a forward process that results…
Graph clustering, which aims to divide a graph into several homogeneous groups, is a critical area of study with applications that span various fields such as social network analysis, bioinformatics, and image segmentation. This paper…
We prove well-posedness for very general linear wave- and diffusion equations on compact or non-compact metric graphs allowing various different conditions in the vertices. More precisely, using the theory of strongly continuous operator…
Generation of graphs is a major challenge for real-world tasks that require understanding the complex nature of their non-Euclidean structures. Although diffusion models have achieved notable success in graph generation recently, they are…
The capability of generalization is a cornerstone for the success of modern learning systems. For non-Euclidean data, e.g., graphs, that particularly involves topological structures, one important aspect neglected by prior studies is how…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
Immersions of graphs to the projective plane are studied. A classification of immersions up to regular homotopy is given. A complete invariant of immersions up to regular homotopy is constructed. Equivalence classes are described.
A diffusion taking value in probability measures on a graph with a vertex set $V$, $\sum_{i\in V}x_i\delta_i$, is studied. The masses on each vertices satisfy the stochastic differential equation of the form $dx_i=\sum_{j\in…